Question

The product of positive numbers is 48. The larger number is 13 more than the smaller. What are both numbers?

Answer 1

Larger number: `16`
Smaller number `3`

Explanation:

Suppose the larger number is `a` and the smaller number is `b`.
You solve the following system of equations:
`a*b=48`
`a-13=b`

Since `b` is `a-13`, you can plug that into `a*b=48`, so...
`a*(a-13)=48`
`a^2-13a=48`
`a^2-13a-48=0`

Factor the polynomial:
`(a-16)(a+3)=0`
`a=16 or a=-3`

`a` is positive so `a=16`.

We can now solve for `b` by plugging in `a`, so...
`16-13=b`
`3=b`

We have `a=16` and `b=3`, meaning that
the larger number is `16` and the smaller number is `3`.